Linear Combination...

Is Algebra 2 Easy For You????

• Kinda

• Total voters
3

stumped_by_math000

New member
1- ---( 5x+y=6 )
( -5x+3y=-22 )

2- ---( 2x-3y=8 )
( 8x+3y=1 )

Okay, I have to 'use linear combination' to solve these systems,
but I don't understand how to do it. Can you help me :?:

smileyborg

New member
Hey.

All linear combination means is a method of solving 2 equations with 2 variables.

If you have 2 variables like x and y, you need 2 equations to solve for each.

So, there are two ways:

linear combo
and
substitution

I won't go into substitution now...

anyways,

All you are trying to do in linear combo is get rid of one of the variables (cancel it out) so you can solve for the other. Then you take the one you just solved for and plug it back in to get the other variable.

like this:

2x + y = 4
x + y = 3

You have 2 variables, x and y.

Try to "tweak" one equation so you can add or subtract it to the other equation and one variable will go away...

Try multiplying the second equation by 2.

2x + y = 4
2x + 2y = 6

Then subtract downwards (2x - 2x cancels out...)

(2x + y = 4)
- (2x + 2y = 6)

-y = -2

Divide by -1

y = 2

Now for x, just plug the y answer you just found (2) into any y you see in either of the original equations...

x + y = 3

x + (2) = 3

Subtract 2

x = 1

And you've got the x value!

Usually the answer should be in a coordinate form, so write it as

(x, y)

which is...

(1, 2)